Near-space-gliding vehicles have variable maneuver modes and dramatic changes in their ballistic parameters, which lead to a need to accurately predict an intercept point based on predictions of their trajectories. First, a trajectory prediction method builds a set of time-varying maneuver models based on flight missions combined with an adaptive grid to infer maneuver modes. An interactive multiple-model method of variable structure is proposed to identify the characteristics of the maneuver mode by introducing a fading factor and the modified Markov probability transfer matrix and then predict the trajectory through numerical integration. In the midcourse guidance method, the prediction of the target trajectory is introduced, and the zero-control interception manifold with intersection angle constraints is designed as the midcourse guidance terminal constraint. For the calculation of the starting time of the boost phase, the optimization solution satisfying the remaining flight time constraint is realized based on the Newton-Raphson iterative method. The analytical expression of a guidance command based on zero-error-miss/zero-error-velocity is established on the basis of the optimal control theory to provide an optimal flight path guiding an NSGV fly toward a point of interception. The simulation results show that the trajectory-prediction method has high prediction accuracy and strong convergency for typical maneuver modes, and the proposed midcourse guidance algorithm meets the requirements of the zero-effort intercept manifold with the intersection angle constraints, which is of important theoretical significance and acts as a reference value for intercepting high-velocity maneuver targets.